Coarse information design - Qianjun Lyu; Wing-chuen Suen; Yimeng Zhang (University of Bonn and University of Cologne, Reinhard Selten Institute (RSI), 2024)
We study an information design problem with continuous state and discrete signal space. Under convex value functions, the optimal information structure is interval-partitional and exhibits a dual expectations property: each induced signal is the conditional mean (taken under the prior density) of each interval; and each interval cutoff is the conditional mean (taken under the value function curvature) of the interval formed by neighboring signals. This property enables an examination into which part of the state space is more finely partitioned. The analysis can be extended to general value functions and adapted to study coarse mechanism design.
Keywords: D81; D82; D83; 330; dual expectations; scrutiny; S-shaped value function; coarse nonlinear pricing; energy efficiency ratings